italy...couch? floor? anywhere to sleep? for october

so I'm going to be in italy (mainly florence but i plan on taking trips to as many other places as i can manage) the first 2 weeks of october, and im looking for anywhere i can find to sleep. if youve got a floor, a couch, a bed, a from yard, ANYTHING you can offer to this wandering dreamer trying to escape the monotony of philadelphia, i would be extremely grateful and gladly return the favour to anyone coming to the usa.

other than that, if anyone has any tips on the cheapest sleeping arrangements youve found in italy, it would be much appreciated.